# Euclidean Rings

### Description

The cardinality of the set of units, and of the set of equivalence classes of primes in non-trivial Euclidean domains is discussed with reference to the categories "finite" and "infinite." It is shown that no Euclidean domains exist for which both of these sets are finite. The other three combinations are possible and examples are given. For the more general Euclidean rings, the first combination is possible and examples are likewise given. Prime factorization is also discussed in both Euclidean rings and Euclidean domains. For Euclidean rings, an alternative definition of prime elements in terms of associates is compared and ... continued below

iv, 32 leaves

### Creation Information

Fecke, Ralph Michael May 1974.

### Context

This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 26 times . More information about this thesis can be viewed below.

## Who

People and organizations associated with either the creation of this thesis or its content.

### Rights Holder

For guidance see Citations, Rights, Re-Use.

• Fecke, Ralph Michael

### Provided By

#### UNT Libraries

The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.

## What

Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.

### Description

The cardinality of the set of units, and of the set of equivalence classes of primes in non-trivial Euclidean domains is discussed with reference to the categories "finite" and "infinite." It is shown that no Euclidean domains exist for which both of these sets are finite. The other three combinations are possible and examples are given. For the more general Euclidean rings, the first combination is possible and examples are likewise given. Prime factorization is also discussed in both Euclidean rings and Euclidean domains. For Euclidean rings, an alternative definition of prime elements in terms of associates is compared and contrasted to the usual definitions.

iv, 32 leaves

### Identifier

Unique identifying numbers for this thesis in the Digital Library or other systems.

### Collections

This thesis is part of the following collection of related materials.

#### UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this thesis?

## When

Dates and time periods associated with this thesis.

• May 1974

### Added to The UNT Digital Library

• June 24, 2015, 9:39 a.m.

### Description Last Updated

• Sept. 26, 2016, 2:14 p.m.

Yesterday: 0
Past 30 days: 3
Total Uses: 26

## Interact With This Thesis

Here are some suggestions for what to do next.